Calibrations and T–Duality

For a subclass of Hitchin’s generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated submanifolds minimise a functional occurring as D–brane energy in type II string theories. Further, we investigate the behaviour of calibrated cycles under T–duality and construct non–trivial examples.